Estimation! Estimation! Estimation!
By Bill Reed
The ability to use estimation is the most important math skill anyone can use and master. Using estimation can alleviate so many silly mistakes and erroneous calculations. Estimation helps us confirm reasonable solutions, stay within our budget or spending limits, and yes, even arrive at our destination on time.
We all have that friend who is ALWAYS late! You know exactly who I am talking about, don’t you? Estimation can keep you from being that habitually late person we all know and get frustrated by frequently. Knowing simple facts like 60 m.p.h is 1 mile every minute. Thus 30 m.p.h. is 1 mile every 2 minutes. If you are in town, a good estimate is the number of miles times 2 or 3. That is about how long it will take you to get there (depending on traffic). If you are going by interstate, you can calculate a minute for every mile and you will be very close to your arrival time.
Estimation can help you not be that person who doesn’t have the funds to pay for everything you have purchased. You know who I am talking about. The person at the front of a long line of people waiting to check out, realizing they do not have the funds to pay for everything. They start taking an item at a time off until they can afford the purchase. Estimation can prevent you from putting yourself in a position you would not want to be in.
Using good estimation skills can save you from so many disastrous and embarrassing situations. If you get good at making reasonable estimates, not only will you look very intelligent, it can save you time and money! Let’s delve into estimation skills.
What is Estimation?
What does it mean to use estimation and why is it so important you ask? Webster’s defines Estimation as:
- a) rough or approximate calculation, b) a numerical value obtained from a statistical sample and assigned to a population parameter
- a statement of the cost of work to be done
- an opinion or judgment of the nature, character, or quality of a person or thing
Did you know that there are three different types of estimation? They are:
- Measurement estimation- finding an approximate measure without making an exact measurement.
- Quantity estimation- finding an approximate number of items in a collection.
- Computational estimation- finding a number that is an approximation of a computation that we cannot or do not wish to determine exactly.
Where to Start
To complete all three types of estimation you need an anchor point. The anchor point is the piece of information or knowledge that will be your reference for your estimations. Basically, the anchor point answers the question; “How did you arrive at your estimation?” Teachers need to ask about this anchor point so they know a student’s estimation is accurate or even reasonable.
I learned how important the anchor point is when we live in Northern California. Being from Indiana, when you ask how far away a destination is from you, you receive an estimation in miles. I know what a mile is and how long it takes me to travel a mile. In California, when you ask how far away a destination is you get a time reference. I never thought about asking for an anchor point for the time reference. That was a big mistake on my part.
When I asked a friend, “How far is Disneyland from us?”, they responded, “About 8 hours.” I thought to myself, OK, I can drive that in a day no problem. When my family and I drove to Disneyland, it took us almost 12 hours! I learned a very valuable lesson from this experience. It taught me to ALWAYS ask for the person’s anchor point. Hindsight led me to the conclusion that I would NEVER ride with my friend on a long road trip!
I learned from this experience. I now always ask students, “How did you come up with your estimation?” This way I know if their estimation is accurate and reasonable. If I had asked my friend the simple anchor point question, “How fast do you drive?” I would have known they were Danica Patrick and would have fared quite well in the Indianapolis 500!
Integrating Estimation Practice
Estimation is a skill that needs to be taught and practiced regularly in the classroom. It is a skill that ALL students at ALL levels need to use! Teachers need to be asking students questions that practice and enhance their estimation skills. Check out this great resource with tons of fun ideas. There are so many opportunities for teachers to integrate estimation into the lesson. Sometimes an opportunity can be as simple as asking what a reasonable answer would be for the problem the student is working on (not the answer but a range for a reasonable answer). Other examples present themselves in a teachable moment.
A student in my first-period Pre-Calculus class was constantly 5 – 10 minutes late to class. First-period was the only period they were tardy to class. I asked the student if it would be ok to use this as a warm-up math problem. They agreed. The next day the warm-up problem on the board when students arrived was; “Approximately, how long should it take you to drive to school? Explain your estimation.” When we debriefed the warm-up, most students knew about how far they lived from school. What many did not know was what was the anchor point for this estimation. Thus the answers were all over the place from way too short to way too long.
This simple activity led to a great discussion with my Pre-Calculus students for how important using estimation is to get a reasonable solution. By the way, after that day in early October, the habitually tardy student was only late 1 more time all year! Using estimation came into play so many times the rest of the year for my Pre-Calculus students. They were much better at finding trig function values, zeros, limits, and sketching graphs.
Teachers must make this a priority! Teachers must be asking for reasonable estimates BEFORE they ask for the actual solution! It is apparent that this is not happening, when you see what is being reported by the media, politicians, and financial analysts. Too many times the estimations are not reasonable and do not even make sense! This is why it is so very important to always ask students and anyone for that matter, “How did you arrive at that estimation?”. When you ask this question you will find, all too often, that it is not really an estimation. It is just a total guess.
Asking students to make estimations and reasonable calculations like this is an invaluable skill. The more practice students get with their estimation skills the better their estimation skills become. A similar estimation question for teachers to consider asking students to work. What would millions of people look like if they were all in one place? Asking students to explain their process and their thinking is imperative. That is the key to getting students to develop their estimation skills.
When students start to get good and practice their estimation skills, you can start to ask them if they think their estimate is too high or too low? Then ask them how they knew if their estimate was too high or too low. Ask them why they used their method to come up with their estimation. You will see that when students are asked to explain their thinking and process for their estimation their calculation skills will greatly improve. Their understanding of the math concepts they are working on will improve. Using estimation and asking students to explain how they arrive at their estimation has so many positive attributes in students learning mathematics.
Estimation is one of the best ways for everyone, young and old, to keep their math skills sharp and have the ability to get reasonable answers to so many questions. If you have never seen or used them, Fermi Problems are a great way to keep estimation skills sharp! Fermi Problems are problems where you cannot get an exact answer. Students must find a good anchor point and all their skills of estimation to solve any Fermi Problem.
I will leave you with a wonderful resource where you can learn more about Fermi Problems, get students actively involved in excellent estimation skills, and enjoy working on rich mathematical tasks that enhance what you are teaching and students are learning. Check out this resource at Fermi Problems – Estimation at its very best! Have fun and enjoy using estimation to solve these problems!
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