In a Football Field?

(An Estimating Activity)

- Mathematics

--Algebra

--Applied Math

--Arithmetic

--Measurement - Social Studies

--Geography

- 3-5
- 6-8
- 9-12

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

- build/reinforce estimating skills.
- solve a problem by taking a sample count of blades of grass.
- calculate accurately to solve the problem.

estimate, football, calculate, sample

- a cardboard frame, the inside of which measures 1 square foot

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:

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.How many blades of grass are on a football field?

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

- Arrange students into pairs.
- Present each pair of students with a cardboard frame, the inside of which measures 1 square foot (12 inches x 12 inches).
- Ask students to suggest how the frame might help them solve the problem. Some students will likely suggest that they will count the number of blades of grass inside the frame. Then multiply that number by 48,000.
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. - Now it's time for students to start counting! Each team of students will work together to determine the number of blades of grass in their 1-square-foot sample. Then they will multiply that number of blades of grass 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**

- Figure the average of the student teams' estimates.
- Might using a 3-inch square frame have changed the end result? Would it have made the estimates any more accurate? In that case, students would

--- count the number of blades of grass in a 3-inch-square frame.

--- multiply that number times 16 (the number of 3-inch squares in a square foot) to determine the number of blades of grass in 1 square foot.

--- multiply that number times 48,000 to determine the number of blades of grass on the field. - See an additional "extend the lesson" idea in the Assessment section below.

You might pose another problem as a follow-up activity. Present students with the following information:

- Total world population: 6,525,000,000 (source [July 2006 estimate])
- Total habitable land on Earth: 52,000,000 square miles (source)

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,

- North America has 32 people per square mile
- South America has 73 people per square mile
- Europe has 134 people per square mile
- Asia has 203 people per square mile
- Africa has 65 people per square mile
- Australia has 6.4 people per square mile

**More info from about.com:**

- Canada's population density is 9.27 people per square mile.
- Monaco has the world's highest population density: 43,000 people per square mile.
- Since Monaco has a high density due to its extremely small size, Bangladesh is often considered the most densely populated country: 2,200 people per square mile.
- Mongolia is the world's least densely populated country: 4.3 people per square mile.
- About 90 percent of Earth's people live on 10 percent of the land.
- About 90 percent of Earth's people live north of the equator.

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

See more Lesson Plans of the Day in our Lesson Plan of the Day Archive. (There you can search for lessons by subject too.)

For additional math lesson plans, see these Education World resources:

For additional social studies lesson plans, see these Education World resources:

- Lesson Planning: Social Studies
- Social Studies Subject Center
- Teacher-Submitted Lesson Plans: Social Studies
- More Geography Lesson Ideas
- Geography A to Z
- Where in the World Is Mrs. Waffenschmidt?
- Mystery State

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Copyright© 2009 Education World

Originally published 05/12/2006

Last updated 04/29/2009