The technologically based data driven world in which we live in has made STEM (Science, Technology, Engineering, and Mathematics) education and STEM careers of great importance. There are certain STEM fields and occupations where the need for workers is expected to be greatest. The fastest growing jobs include statisticians, operations research analysts, forensic science technicians, biomedical engineers, mathematicians, computer systems analysts, actuaries, software developers, and information security analysts.
Because there is such a high need for skilled professionals at all educational levels there is a shortage of STEM workers who have either associate degrees or attended trade school (Xue & Larson, 2014). There are two careers which usually require an associate degree, one is a computer user support specialist, which is expected to grow by 12.8% and the other is a web developer which is predicted
to grow by 26.6% from 2014 to 2024 (Fayer et al., 2017).
The government and government-related sector has shortages in specific areas such as nuclear engineering, materials science, electrical engineering, cybersecurity, and intelligence. This is not necessarily because of lack of STEM professionals but due to the lack of STEM professionals who are U.S. citizens (Xue & Larson, 2014). This is often criteria for employment that requires certain security clearances.
The private sector has shortages with petroleum engineers in certain geographic locations, data scientists, and software developers (Xue & Larson, 2014).
There is also demand for STEM skills below the bachelor’s level. A 2011 survey of manufacturers found that as many as 600,000 jobs remain unfilled due to lack of qualified candidates for technical positions requiring STEM skills, primarily in production (machinists, operators, craft workers, distributors, and technicians) (The Manufacturing Institute and Deloitte, 2011). While the
number of job openings in this sector has decreased since 2011, there were still 264,00 opening in 2014 (BLS, 2014).
Maiorca, C., Stohlmann, M., & Driessen, M. (2019). Getting to the bottom of the truth: STEM shortage or STEM surplus? In A. Sahin & M. Mohr-Schroeder (Eds.). Myths and Truths: What Has Years of K-12 STEM Education Research Taught Us? (pp.22-35). Boston, MA: Brill.
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.
Battleship is a game of guessing, strategy, and logical thought. Students use their mathematical knowledge to set up their ships; then play against another person to be the first to sink their opponent's ships. Below are instructions for one version of the game Battleship.
Setting up your ships
To start, set up your grid so that it will be consistent for all players. Set the x-axis and y-axis to go from -15 to 15.
You will get three ships. The ships will be inputted as linear equations into desmos in the form of y = mx + b. For example y = 4x – 2. To determine the length of your ships you will need to either set the domain (x-values) or range (y-values) with the domain or range being 2 units, 3 units, and 4 unit intervals. (See example below).
Playing the game
You will alternate turns until all of your opponent's ships are sunk. Your torpedoes to sink your opponent's ships will come in the form of circles. If any part of the circle or inside of the circle touches a ship, that ship is sunk. The torpedoes will have different radiuses based on a roll of the dice. You will roll the dice before every turn.
If you roll a:
1- radius of 1
2 - radius of 2
3- radius of 3
4 – radius of 4
5 – radius of 5
6- radius of 6
You get to pick the center of your circle which can be any point in the grid. For the equation of a circle, the center of the circle is (h , k) and the radius is r.
The example below shows two hits and one miss. It will likely take more turns to sink ships, but this is just an example. The equations for each circle are inputted into desmos in the fourth, fifth, and sixth, lines. You should keep track of your opponent's equations in one Desmos window and your equations in another Desmos window.
Click on the following link for other versions of Battleship that can be played with Desmos.
Stohlmann, M. (2017). Desmos battleship. The Australian Mathematics Teacher.
Scale the Strat
Mathematical modeling is garnering national and international focus due to the many benefits that it can provide to students including increased engagement, understanding through multiple representations, and discourse.
The Scale the Strat activity is connected to health science and an event held in Las Vegas sponsored by the American Lung Association, whose mission is to save lives by improving lung health. Each year at the Stratosphere Tower people climb up 108 floors of the tower consisting of 1,455 stairs to raise money for the American Lung Association. Shaun Stephens-Wale has the fastest time running up the stairs in 7 minutes and 3 seconds. At the start of this problem a video is shown about the event.
The question is then posed if Stephens-Wale would beat someone in an elevator to the top of the tower. Students realized that someone in an elevator should arrive at the top first.
The question for the problem is then posed. How many floors would someone in an elevator have to be stopped at in order to tie Stephens-Wale running up the stairs? This problem is connected to creating equations that describe numbers or relationships. In figuring out this problem students make different assumptions and approximations including if the elevator is being used by guests of the casino or staff, the speed of the elevator, and the time it takes for people to get on or off the elevator at each stop. Students have also used the Internet to help develop their solution.
An example solution involves making an assumption that the elevator takes 1.5 seconds to go up each floor and approximately 17 seconds of wait time for each floor it stops at. This takes into account people getting on and off the elevator. The equation would be the following then:
423 = 108 (1.5) + 17x which when solved gives about 15 floors with stops. In this activity the importance of choices and assumptions are highlighted for mathematical modeling.
Stohlmann, M. (2020). STEM integration for high school mathematics teachers. Journal of Research in STEM Education, 6(1), 52-63.
Christian, author, and professor of mathematics education.