Go Ahead, Take a Guess! Estimating in the Real World
Learning how to use estimating to solve real life problems can be a great way for students to apply math skills.
By Jacqueline Dwyer
One of the most useful, yet undervalued, math concepts is estimating. It is a practical skill for use in finding solutions to real-world problems and contributing to higher level math reasoning. Estimation teaches children to use their existing knowledge to figure out a problem. It is more concerned with the thought process that lies behind an answer, than it is with the answer itself.
Enrico Fermi was one of the most famous estimators of all time. He was a Nobel Prize-winning physicist who was known for his ability to perform rapid approximations in his head, using very little data. He developed a set of “Fermi Questions” that are based on making simple, educated estimates for each step of a problem, in order to come up with a reasonable solution. Many of his questions can be found online. These questions can be tailored to suit your child’s age, ability, and interests. Their beauty lies in the fact that there are no wrong answers, only logical answers.
One question my son and I considered was, “What is the circumference of the Earth?” This problem might appear difficult at first glance, but we broke it down into manageable parts. We looked up any figures we didn‘t know, and rounded them. We asked questions like, "How many time zones are there between New York and Los Angeles (3)? Then we estimated how many miles it is over this distance (3,000)? Therefore, there are 1,000 miles per time zone. How many times zones are there around the world? There are 24, because there are 24 hours in a day. This brought us to estimate the miles around the world as being, 24 time zones x 1,000 miles per time zone = approximately 24,000 miles. In reality, the exact circumference of the Earth is 24,901.55 miles at the equator. It is slightly less between the poles. Surprisingly, our estimate was fairly close!
Fermi questions are perfect for math-phobic students, teachers, or parents, because they instill confidence and resourcefulness. Recalcitrant learners are more likely to embrace this skill because there is not pressure to have an exact answer. Estimating can be taught in creative ways, please see the links below.
Lessons on Estimating
Students estimate the average number of listings found in the White Pages of the local telephone directory. They write an explanation of the math processes used to arrive at the final estimate.
Students analyze the differences between guessing and estimating, using jellybeans in various containers.
This is a great lesson for older students on estimating numbers. Students define key vocabulary terms and learn about truncation, front-end estimation, and how to round to appropriate place value.
In this lesson, students develop their estimation skills while evaluating their television-watching habits. By comparing data about the number of hours of television (and commercials) they watch compared to hours spent on other activities, they will draw conclusions about the influence of television in their lives.