Estimating crowd size
To introduce the crowd estimation problem play the video below up to the 1 minute 30 second mark.
Estimating Crowd Size
Thousands of people are on the Las Vegas Strip and in downtown Las Vegas each year to celebrate the birth of the new year. A massive fireworks show begins at midnight. According to the Las Vegas Convention and Visitors Authority, more than 318,000 visitors were in Las Vegas for New Year's Eve in 2019. This is the number of people that visited Las Vegas on New Year’s Eve but not the number of people that are out on the street of the Las Vegas Strip. Las Vegas Boulevard is closed for car traffic on New Year’s Eve so people can walk on the Boulevard.
Is it possible to get an accurate count of the number of people on the street of the Las Vegas Strip on New Year’s Eve? What do you need to do this?
Let’s look at just the crowd on Las Vegas Boulevard in front of the Bellagio.
-What is your estimate of the crowd in front of the Bellagio?
-What is your estimate for the lowest possible number of people?
- What is your estimate for the highest possible number of people?
Problem statement: Consider just the area from Flamingo Road to the Cosmopolitan. Determine a mathematical estimate of the number of people on Las Vegas Boulevard on New Year’s Eve.
Follow up question: The Las Vegas strip is about 4.2 miles long. How many people are on the complete strip on New Year’s Eve?
New Year’s Eve on the Las Vegas Strip is an exciting time and attracts large crowds. In this activity students estimate the number of people that are on Las Vegas Boulevard on New Year’s Eve. This is an engaging and relevant activity with multiple possible solutions and methods. Students can use a variety of mathematics in their solutions including area, measurement, proportional thinking, conversions, estimation, and mathematical operations. Students can also use the Internet as a resource to research information. Given the current COVID-19 pandemic teachers can decide whether students will solve the problem based on past crowds on New Year’s Eve in Las Vegas or with social distancing guidelines in place.
Elementary students may measure off a grid on the floor and see how many people could fit in the grid. They could then use the measure distance feature on google maps to calculate the area on the Las Vegas Strip. Students could divide the area of the strip by the area of the grid they used on the floor. This would provide the number of same-sized grids the students used that would fit on the strip. Students could use this number to multiply by the number of people they fit in their grid.
At the middle school level students may make use of the scale on the provided map to help calculate the area on the strip. They might use the Internet to help determine how many people fit into a certain square footage. They could then determine an estimate of the number of people on the strip.
While using similar methods as above high school students may consider more factors in their estimate. They may adjust their estimate so there is space for people to walk along the strip and then space for people who are staying in one place. They might also consider that there are barriers, trees, and a median where people could not stand. High school students may also come up with a formula for people per square foot based on the type of event or the density of a crowd. The follow-up question would require students to convert measurement units to solve. Limiting the number of people allowed to walk on the street would allow for social distancing to be followed. This would adjust the crowd estimate by just considering the maximum number of people who could safely be on the boulevard at one time.
After teachers have facilitated a discussion of students’ ideas, teachers can also share information about the Jacobs Crowd Formula. Herbert Jacobs, who was a journalism professor at the University of California, Berkeley in the 1960s came up with general guidelines for estimating crowds. He determined that generally a light crowd has one person per 10 square feet, a dense crowd has one person per 4.5 square feet, and a mosh pit like crowed has 1 person per 2.5 square feet. Jacobs became interested in investigating crowd estimation after looking out his office window and noticing crowds of students on the plaza below. The plaza’s concrete was poured in a grid so he used the grid and the number of students in each grid to begin to thinking through a way to estimate crowd size. Students can be asked what are the limitations of this method and the methods that they came up with. Students can also be asked in what situations estimating crowd size is used.
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Christian, author, and professor of mathematics education.