By taking a sample count from a small area, students will be able to estimate the total number of blades of grass in a football field.
Students
estimate, football, calculate, sample
This lesson is a good fall or springtime lesson. It's also an excellent lesson for the last days of the school year because it will involve students in doing real math with a fun purpose.
Have you ever heard someone say in response to a difficult task "That's as hard as counting blades of grass" or "I'd rather count blades of grass." In this lesson, students will do just that!
Present the following problem to students:
How many blades of grass are on a football field?At first glance, this might appear a daunting question. But if students think for a moment, they might be able to come up with a plan that will enable them to estimate, fairly accurately, the number of blades of grass on a football field. Invite them to suggest some possible ways in which they might accomplish that goal.
An alternative problem might be to pose a question that focuses on your own school. For example, How many blades of grass are in the front yard (or another area) of our school?
After students have shared some possible approaches, introduce them to the lesson
Why 48,000?
For the purpose of this activity we have used this diagram to calculate the square footage of a football field. We have counted the amount of turf on the playing area excluding the two end zones. The area of the field is 100 yards long and 53-1/3 yards wide, or 300 x 160 feet long. We multiplied 300 x 160 to learn the total number of square feet on a football field (48,000).
So, to figure the total number of blades of grass on a football field, students will count the number of blades of grass in a 1-square-foot sample and multiply that times 48,000.
After students have done that, provide time for them to share their blade counts, calculations, and estimates. How close -- or far apart -- were the teams' estimates?
Note: If you decided to challenge students to estimate the number of blades of grass on an area of grass on your school property instead of a football field, you will need to measure the length and width of the property and multiply those measurements to determine the number of square feet. That number will be the multiplier (instead of 48,000) when your students do their calculations.
Extend the Lesson
You might pose another problem as a follow-up activity. Present students with the following information:
Then pose this question:
If the world population was evenly distributed over Earth's habitable land, how many people would live on each square mile of Earth? [The world population (6,525,000,000) divided by the number of habitable square miles of land (52,000,000) reveals that the total number of people per square mile would be approximately 125.]
How does that compare with the number of people per square mile in your state? the United States? other countries around the world? Here is some sample data for making comparisons...
According to about.com,
More info from about.com:
EducationWorld.com
Gary Hopkins
MATHEMATICS: Number and Operations
GRADES 3 - 5
NM-NUM.3-5.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.3-5.3 Compute Fluently and Make Reasonable Estimates
GRADES 6 - 8
NM-NUM.6-8.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.6-8.3 Compute Fluently and Make Reasonable Estimates
GRADES 9 - 12
NM-NUM.9-12.1 Understand Numbers, Ways of Representing Numbers, Relationships Among Numbers, and Number Systems
NM-NUM.9-12.3 Compute Fluently and Make Reasonable Estimates
MATHEMATICS: Measurement
GRADES 3 - 5
NM-MEA.3-5.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.3-5.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements
GRADES 6 - 8
NM-MEA.6-8.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.6-8.2 Apply Appropriate Techniques, Tools, and Formulas to Determine Measurements
GRADES 9 - 12
NM-MEA.9-12.1 Understand Measurable Attributes of Objects and the Units, Systems, and Processes of Measurement
NM-MEA.9-12.2 Apply Appropriate Techniques, Tools,
and Formulas to Determine Measurements
MATHEMATICS: Problem Solving
GRADES Pre-K - 12
NM-PROB.PK-12.1 Build New Mathematical Knowledge Through Problem Solving
NM-PROB.PK-12.2 Solve Problems That Arise in Mathematics and in Other Contexts
NM-PROB.PK-12.3 Apply and Adapt a Variety of Appropriate
Strategies to Solve Problems
MATHEMATICS: Connections
GRADES Pre-K - 12
NM-CONN.PK-12.3 Recognize and Apply Mathematics in
Contexts Outside of Mathematics
MATHEMATICS: Representation
GRADES Pre-K - 12
NM-REP.PK-12.1 Create and Use Representations to Organize, Record, and Communicate Mathematical Ideas
NM-REP.PK-12.3 Use Representations to Model and
Interpret Physical, Social, and Mathematical Phenomena
SOCIAL SCIENCES: Geography
GRADES K - 12
NSS-G.K-12.1 The World in Spatial Terms
NSS-G.K-12.2 Places and Regions
NSS-G.K-12.6 Uses of Geography
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Copyright© 2009 Education World
Originally published 05/12/2006
Last updated 04/29/2009