Back of the Envelope Calculations Prepare Students for Real World Statistics

At the Academy at Penguin Hall, young women are given the wonderful opportunity to take risks, grow, and flourish in a safe and supportive environment. With a student-centered approach and interdisciplinary learning, students are encouraged in their pursuit of not only intellectual, but also social, athletic, spiritual, and personal development. Teachers integrate real-world issues into their classroom projects and discussions in order to empower and prepare students to thrive once they leave the academy.

In the Critical Explorations of Modern Issues class, known as “Crit”, Teacher Sherry Cook recently presented her students with a project to challenge their perception and understanding of statistics. With an overload of media and information available in today’s world, statistics appear everywhere in life, from cereal boxes to Facebook posts. While many statistics are accurate, data can often either be skewed or misrepresented to espouse or encourage a certain point of view. Ms. Cook created a fun, interactive project to enable students to discern reasonable statistics from ones that appear to be flawed.

The concept of a “back of the envelope calculation” was embraced using a variety of envelopes prepared with a statistical claim printed on the front. Envelopes were given to students at random times throughout the week — in the lunchroom, on the way to class, in a class — in an effort to simulate the real life experience of hearing statistics and numerical claims throughout the day. Students were handed an envelope and asked to declare the statistic as either “plausible” or “fishy”. By using data that they knew to be true, in addition to well-informed estimates, students flipped their envelopes over and crunched through a couple of calculations in an effort to get a sense of the validity of the statistic. They were not allowed to use technology to answer their questions.

For example, one envelope read,

“In an effort to increase awareness of the need for unrestricted birth control for high school students, an organization posted the following statistic on their website:
Every year in the United States, one million babies are born to teen girls.
Does this sound right?”


We only need to know a couple of benchmark statistics in order to make sense of most of the claims we hear. One such benchmark is that four million babies are born in the US every year. Students were able to use that fact to consider whether it makes sense that one quarter of all babies are born to teenage mothers. Some students reasoned from the basic fact, others used the fact to get a sense of just how many teens girls there are in the US: There are 7 teen age groups (13-19) and if about 4 million babies are born then there are about 28 million teens, half of which are female …. and so on.

Projects like these allow students to think critically and integrate what they learn into real-world problems, and equip them with skills that they will use for the rest of their lives. This unique approach of providing students with the opportunity to use what they learn in applicable ways is one of the many aspects that sets the Academy at Penguin Hall apart from many traditional approaches to education. By combining what they learn in their classes with relevant issues, the young women here will no doubt be prepared for whatever comes their way, whether they have the back of an envelope with them or not.

Are you ready for the back of the envelope challenge? Our students are…