DESCRIPTION OF ACTIVITY (BASEBALL GEOMETRY)
In this activity, students will learn the specifications of a modern baseball. They will also learn that the materials used inside and out have been tested, alternately resulting in advantages to pitchers and to batters.
Technology Integration
Students will be using the visual aid of an overhead transparency board to help them find the area of the baseball.
STUDENT LEARNING OUTCOME
Students will:
Source:
http://www.pbs.org/kenburns/baseball/teachers/lesson4.html
COMMON CORE STANDARD
7.G.1 Solve problems involving scale drawings of geometric figures,
including computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale.
Source:
http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
MATERIALS
DIRECTIONS
1) Give every student a baseball for the activity.
2) Each student spreads out Play-Doh "pie crust style" on the wax paper.
3) Rolling the baseball in the Play-Doh, make an impression of the "footprint" shape of the stitching pattern.
[** This pattern might also be called a "peanut" shape. Mathematically, it is an "Oval of Cassini" where k<b and for two foci F1(-b,0) and F2(b,0) and any point P on the curve, the product of the distances from the foci to the point P is equal to the value of k squared, or PF1xPF2 = k^2. More on this can be found in many Handbooks of Mathematics Tables and Standards. For an Interactive Online model where students can "drag and drop" the foci to see changes in the Oval of Cassini, go to the University of Illinois Web sitehttp://chickscope.beckman.uiuc.edu/explore/eggmath/
shape/cassini.html.]
4) Ask students if they realize the covering of the baseball is actually two of these "footprints" stitched together?
5) Place the overhead transparency of the square centimeter grid over this impression.
6) Check this work using another method. Wrap a string or tape around the center of the baseball to find its circumference. Divide this circumference by PI = 3.14 to find the diameter. Take half of the diameter to find radius.
7) Using r = radius and S = Surface Area, the formula for the surface area of a sphere is S = 4 * Pi * r^2
8) Have students get together in small groups to discuss their results.
9) Then have the whole group get together to report out their results and what they have learned.
SUPPLEMENTARY READING MATERIALS AND INTERNET SOURCES TO EXTEND STUDENTS' UNDERSTANDING OF THE CONTENT
Click here to learn more about Baseball History.
Click here to watch and learn about circles.
Click here to read about diameter.
Click here to read about baseball player Jackie Robinson.
***To view rubric for this activity, please click on our site's ACTIVITY SHEETS tab.
In this activity, students will learn the specifications of a modern baseball. They will also learn that the materials used inside and out have been tested, alternately resulting in advantages to pitchers and to batters.
Technology Integration
Students will be using the visual aid of an overhead transparency board to help them find the area of the baseball.
STUDENT LEARNING OUTCOME
Students will:
- be introduced to historical and modern materials and construction of baseballs
- apply various methods for finding volume and surface area of a sphere
- compare and contrast results among these methods
Source:
http://www.pbs.org/kenburns/baseball/teachers/lesson4.html
COMMON CORE STANDARD
7.G.1 Solve problems involving scale drawings of geometric figures,
including computing actual lengths and areas from a scale drawing
and reproducing a scale drawing at a different scale.
Source:
http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf
MATERIALS
- Play-Doh
- String
- Ruler
- wax paper
- baseballs
- overhead transparency with square centimeter grid.
- Baseball innings Shadow Ball, The National Pastime and The Capital of Baseball (recommended but not required)
DIRECTIONS
1) Give every student a baseball for the activity.
2) Each student spreads out Play-Doh "pie crust style" on the wax paper.
3) Rolling the baseball in the Play-Doh, make an impression of the "footprint" shape of the stitching pattern.
[** This pattern might also be called a "peanut" shape. Mathematically, it is an "Oval of Cassini" where k<b and for two foci F1(-b,0) and F2(b,0) and any point P on the curve, the product of the distances from the foci to the point P is equal to the value of k squared, or PF1xPF2 = k^2. More on this can be found in many Handbooks of Mathematics Tables and Standards. For an Interactive Online model where students can "drag and drop" the foci to see changes in the Oval of Cassini, go to the University of Illinois Web sitehttp://chickscope.beckman.uiuc.edu/explore/eggmath/
shape/cassini.html.]
4) Ask students if they realize the covering of the baseball is actually two of these "footprints" stitched together?
5) Place the overhead transparency of the square centimeter grid over this impression.
- Count the number of whole squares completely interior to the footprint. This is a lower bound to the area of the footprint (it is at least this much).
- Take this number and add the number of whole squares that even just touch the footprint. This is an upper bound to the area of the footprint (it is at most this much).
- Average the upper bound and the lower bound to get a best estimate of the area of the footprint.
- Double this area to find the total surface area.
6) Check this work using another method. Wrap a string or tape around the center of the baseball to find its circumference. Divide this circumference by PI = 3.14 to find the diameter. Take half of the diameter to find radius.
7) Using r = radius and S = Surface Area, the formula for the surface area of a sphere is S = 4 * Pi * r^2
8) Have students get together in small groups to discuss their results.
9) Then have the whole group get together to report out their results and what they have learned.
SUPPLEMENTARY READING MATERIALS AND INTERNET SOURCES TO EXTEND STUDENTS' UNDERSTANDING OF THE CONTENT
Click here to learn more about Baseball History.
Click here to watch and learn about circles.
Click here to read about diameter.
Click here to read about baseball player Jackie Robinson.
***To view rubric for this activity, please click on our site's ACTIVITY SHEETS tab.